Titlebook: A Textbook of Algebraic Number Theory; Sudesh Kaur Khanduja Textbook 2022 The Editor(s) (if applicable) and The Author(s), under exclusive

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Beschreibung chemischer Strukturen,In this chapter we discuss the splitting of rational primes in the ring of integers of an algebraic number field. The notions of ramification index and residual degree are also introduced and a fundamental equality is established. A theorem of Dedekind about the splitting of rational primes is proved and several applications are given.

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Chemische Bindung und Gitterenergie,In this chapter, we shall prove a theorem which describes the structure of the group of units of . for an algebraic number field .. It was proved by Dirichlet? in 1846.

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Chemische Bindung und Gitterenergie,The finiteness of the class number of an algebraic number field is established in this chapter using Minkowski’s convex body theorem. Several examples of the computation of class number are given. Also, Hermite’s theorem on discriminant is proved. The chapter concludes with the proof of a special case of Fermat’s last theorem.

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A Textbook of Algebraic Number Theory978-981-16-9150-8Series ISSN 2038-5714 Series E-ISSN 2532-3318

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Beschreibung chemischer Strukturen,tant problems in algebraic number theory. For an algebraic number field . with . in the ring . of algebraic integers of . having .(.) as its minimal polynomial over the field . of rational numbers, the discriminant . of . and the discriminant of the polynomial .(.) are related by the formula . So co

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Chemische Bindung und Gitterenergie,terms of simpler values depending upon the field .. Since all ideals of . are product of prime ideals and the number of prime ideals of . is infinite, to compute . in finite number of steps, one has to use some infinite processes, e.g., infinite series, infinte products and some analytic concepts as